Poissonian asymptotics of a randomly perturbed dynamical system: Flip-flop of the stochastic disk dynamo
type: Item
instance of: scholarly article
title: Poissonian asymptotics of a randomly perturbed dynamical system: Flip-flop of the stochastic disk dynamo
zbMATH Open document ID: 0921.60046
DOI: 10.1007/BF02175555
author: H. M. Ito
author: Toshio Mikami
published in: Journal of Statistical Physics
publication date: 1999-09-21T00:00:00Z
review text: The authors consider random perturbations of the flow generated by the 2-dimensional vector field \((-\mu x_1+x_1x_2,-\nu x_2+1-x_1^2)\) which describes a single-disk dynamo model and has two stable and one saddle type fixed points. They show that when parameter of perturbations tends to zero the process counting the number of transitions between basins of attracting points with properly scaled time converges (in the sense of convergence of finite-dimensional distributions) to a Poisson process. This stochastic disk dynamo model was proposed previously by the first author [J. Stat. Phys. 53, 19-39 (1988)] as a model of reversals of Earth's magnetic field.
reviewed by: Yuri Kifer
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60G55
Mathematics Subject Classification ID: 86A32
zbMATH DE Number: 1279701
zbMATH Keywords: small random perturbations
zbMATH Keywords: Poisson process
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1279701